- Author:
- pmr2.import <nobody@models.cellml.org>
- Date:
- 2006-07-09 07:59:10+12:00
- Desc:
- committing version01 of vangoor_lebeau_krsmanovic_sherman_catt_stojilkovic_2000
- Permanent Source URI:
- http://models.cellml.org/workspace/vangoor_lebeau_krsmanovic_sherman_catt_stojilkovic_2000/rawfile/57e6746b57251c751c1b3921fdc6389142ec24d4/vangoor_lebeau_krsmanovic_sherman_catt_stojilkovic_2000.cellml
<?xml version='1.0' encoding='utf-8'?>
<!-- FILE : vangoor_model_2000.xml
CREATED : 8th May 2002
LAST MODIFIED : 20th April 2005
AUTHOR : Catherine Lloyd
Bioengineering Institute
The University of Auckland
MODEL STATUS : This model conforms to the CellML 1.0 Specification released on
10th August 2001, and the 16/01/2002 CellML Metadata 1.0 Specification.
DESCRIPTION : This file contains a CellML description of Van Goor et al's
2000 mathematical model of amplitude-dependent spike broadening and enhanced Ca2+ signaling in GnRH-secreting neurons.
CHANGES:
19/07/2002 - CML - Added more metadata.
09/04/2003 - AAC - Added publication date information.
20/04/2005 - PJV - Made MathML id's unique
--><model xmlns="http://www.cellml.org/cellml/1.0#" xmlns:cmeta="http://www.cellml.org/metadata/1.0#" xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" xmlns:bqs="http://www.cellml.org/bqs/1.0#" xmlns:cellml="http://www.cellml.org/cellml/1.0#" xmlns:dcterms="http://purl.org/dc/terms/" xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#" cmeta:id="vangoor_lebeau_krsmanovic_sherman_catt_stojilkovic_2000_version01" name="vangoor_lebeau_krsmanovic_sherman_catt_stojilkovic_2000_version01">
<documentation xmlns="http://cellml.org/tmp-documentation">
<article>
<articleinfo>
<title>Amplitude-Dependent Spike-Broadening In GnRH-Secreting Neurons</title>
<author>
<firstname>Catherine</firstname>
<surname>Lloyd</surname>
<affiliation>
<shortaffil>Bioengineering Institute, University of Auckland</shortaffil>
</affiliation>
</author>
</articleinfo>
<section id="sec_status">
<title>Model Status</title>
<para>
This is the original unchecked version of the model imported from the previous
CellML model repository, 24-Jan-2006.
</para>
</section>
<sect1 id="sec_structure">
<title>Model Structure</title>
<para>
During an action potential, depolarisation of the plasma membrane causes voltage-gated Ca<superscript>2+</superscript> channels to open, allowing Ca<superscript>2+</superscript> to diffuse into the cell. The subsequent increase in cytosolic calcium concentration ([Ca<superscript>2+</superscript>]<subscript>i</subscript>) triggers a number of biochemical events involved in the control of cell function. The frequency, amplitude and duration of the Ca<superscript>2+</superscript> signals determine the specificity of the cellular response. However, the exact relationship between the action potential waveform, the gating properties of the voltage-gated Ca<superscript>2+</superscript> channels, the pattern of Ca<superscript>2+</superscript> influx and the ionic mechanisms underlying the the agonist-induced Ca<superscript>2+</superscript> spike broadening has not been characterised. </para>
<para>
In their 2000 paper, Fredrick Van Goor, Andrew P. LeBeau, Lazar Z. Krsmanovic, Arthur Sherman, Kevin J. Catt and Stanko S. Stojikovic examine the ionic mechanism mediating depolarisation-induced Ca<superscript>2+</superscript> spike broadening in GnRH-secreting (GT1) neurons. The validity of their experimental results were tested by comparing them with a computational model. They also used this mathematical model to examine the influence of voltage-gated Ca<superscript>2+</superscript> channel gating properties on the ability of action potential broadening to enhance the I<subscript>Ca</subscript>.
</para>
<para>
Their mathematical model is based exclusively on the on the properties of the individual ionic currents characterised in GT1 neurons. The ionic currents used were a TTX-sensitive I<subscript>Na</subscript>, L- and T-type I<subscript>Ca</subscript>, a voltage sensitive (delayed-rectifying) I<subscript>K(dr)</subscript>, an M-like I<subscript>K</subscript> (I<subscript>M</subscript>), an inward rectifier I<subscript>K</subscript> (I<subscript>ir</subscript>), and a Ca<superscript>2+</superscript> permeable, voltage-insensitive inward leak, I<subscript>d</subscript> (see <xref linkend="fig_cell_diagram"/> below).
</para>
<para>
In their original model, Van Goor <emphasis>et al</emphasis>. used a Hodgkin-Huxley type equation to represent the sodium current. However, in this description, I<subscript>Na</subscript> exhibited a large surge of activation during the spike repolarisation, and it also did not spike during broadening, suggesting that the model gating kinetics didn't accurately represent those in GTI neurons. Consequently, they replaced the Hodgkin-Huxley-like description with Kuo and Bean's 1994 model of I<subscript>Na</subscript> (see <xref linkend="fig_reaction_diagram"/> below). In this description the Na+ channel is composed of subunits with four possible states: deactivated (D), activated (A), deactivated-inhibited (D*), and activated-inhibited (A*). The open, conducting state (O) is given by A3 in the reaction scheme.
</para>
<para>
The complete original paper reference is cited below:
</para>
<para>
<ulink url="http://www.biophysj.org/cgi/content/abstract/79/3/1310">Amplitude-Dependent Spike-Broadening and Enhanced Ca<superscript>2+</superscript> Signaling in GnRH-Secreting Neurons</ulink>, Fredrick Van Goor, Andrew P. LeBeau, Lazar Z. Krsmanovic, Arthur Sherman, Kevin J. Catt and Stanko S. Stojikovic, 2000, <ulink url="http://www.biophysj.org/">
<emphasis>Biophysical Journal</emphasis>
</ulink>, 79, 1310-1323. (<ulink url="http://www.biophysj.org/cgi/content/full/79/3/1310">Full text</ulink> and <ulink url="http://www.biophysj.org/cgi/reprint/79/3/1310.pdf">PDF</ulink> versions of the article are available for Journal Members on the BJ website.) <ulink url="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve&db=PubMed&list_uids=10968994&dopt=Abstract">PubMed ID: 10968994</ulink>
</para>
<para>
The raw CellML description of the model can be downloaded in various formats as described in <xref linkend="sec_download_this_model"/>
</para>
<informalfigure float="0" id="fig_cell_diagram">
<mediaobject>
<imageobject>
<objectinfo>
<title>diagram of the cell model</title>
</objectinfo>
<imagedata fileref="vangoor_2000-celldiagram.png"/>
</imageobject>
</mediaobject>
</informalfigure>
<informalfigure float="0" id="fig_reaction_diagram">
<mediaobject>
<imageobject>
<objectinfo>
<title>diagram of the cell model</title>
</objectinfo>
<imagedata fileref="vangoor_2000.png"/>
</imageobject>
</mediaobject>
</informalfigure>
</sect1>
</article>
</documentation>
<!--
Below, we define some additional units for association with variables and
constants within the model. The identifiers are fairly self-explanatory.
-->
<units name="millisecond">
<unit units="second" prefix="milli"/>
</units>
<units name="per_millisecond">
<unit units="millisecond" exponent="-1"/>
</units>
<units name="millivolt">
<unit units="volt" prefix="milli"/>
</units>
<units name="picoF">
<unit units="farad" prefix="pico"/>
</units>
<units name="picoA">
<unit units="ampere" prefix="pico"/>
</units>
<units name="nanoS">
<unit units="siemens" prefix="nano"/>
</units>
<units name="millimolar">
<unit units="mole" prefix="milli"/>
<unit units="litre" exponent="-1"/>
</units>
<units name="millimolar_per_ms">
<unit units="millimolar"/>
<unit units="millisecond" exponent="-1"/>
</units>
<!--
The "environment" component is used to declare variables that are used by
all or most of the other components, in this case just "time".
-->
<component name="environment">
<variable units="millisecond" public_interface="out" name="time"/>
</component>
<component name="membrane">
<variable units="millivolt" public_interface="out" name="V"/>
<variable units="picoF" name="Cm" initial_value="14.0"/>
<variable units="picoA" name="i_app"/>
<variable units="millisecond" public_interface="in" name="time"/>
<variable units="picoA" public_interface="in" name="i_Na"/>
<variable units="picoA" public_interface="in" name="i_Ca_L"/>
<variable units="picoA" public_interface="in" name="i_Ca_T"/>
<variable units="picoA" public_interface="in" name="i_K_dr"/>
<variable units="picoA" public_interface="in" name="i_M"/>
<variable units="picoA" public_interface="in" name="i_ir"/>
<variable units="picoA" public_interface="in" name="i_d"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="membrane_voltage_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> V </ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<ci> i_app </ci>
<apply>
<plus/>
<ci> i_Na </ci>
<ci> i_Ca_L </ci>
<ci> i_Ca_T </ci>
<ci> i_K_dr </ci>
<ci> i_M </ci>
<ci> i_ir </ci>
<ci> i_d </ci>
</apply>
</apply>
<ci> Cm </ci>
</apply>
</apply>
</math>
</component>
<rdf:RDF>
<rdf:Description rdf:about="#sodium_current">
<cmeta:comment rdf:parseType="Resource">
<rdf:value>
In their original model, Van Goor et al. used a Hodgkin-Huxley type
equation to represent the sodium current (see CellML description
below). However, in this description, INa exhibited a large surge of
activation during the spike repolarisation, and also did not spike
during broadening, suggesting that the model gating kinetics don't
accurately represent those in GTI neurons.
Consequently, they replaced the Hodgkin-Huxley-like description with
Kuo and Bean's 1994 model of INa. In this description the Na+ channel
is composed of subunits with four possible states: deactivated (D),
activated (A), deactivated-inhibited (D*), and activated-inhibited
(A*). The open, conducting state (O) is given by A3 in the reaction
scheme.
Following is the original reaction scheme.
</rdf:value>
<rdf:value rdf:parseType="Literal">
<component name="sodium_current">
<variable units="picoA" public_interface="out" name="i_Na"/>
<variable units="nanoS" name="g_Na" initial_value="60.0"/>
<variable units="millivolt" name="V_Na" initial_value="60.0"/>
<variable units="millisecond" public_interface="in" private_interface="out" name="time"/>
<variable units="millivolt" public_interface="in" private_interface="out" name="V"/>
<variable units="dimensionless" private_interface="in" name="m"/>
<variable units="dimensionless" private_interface="in" name="h"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="i_Na_calculation">
<eq/>
<ci> i_Na </ci>
<apply>
<times/>
<ci> g_Na </ci>
<apply>
<power/>
<ci> m </ci>
<cn cellml:units="dimensionless"> 3.0 </cn>
</apply>
<ci> h </ci>
<apply>
<minus/>
<ci> V </ci>
<ci> V_Na </ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="sodium_current_m_gate">
<variable units="dimensionless" public_interface="out" name="m"/>
<variable units="dimensionless" name="m_infinity"/>
<variable units="millisecond" name="tau_m"/>
<variable units="millivolt" public_interface="in" name="V"/>
<variable units="millisecond" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="sodium_current_m_gate_m_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> m </ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<ci> m_infinity </ci>
<ci> m </ci>
</apply>
<ci> tau_m </ci>
</apply>
</apply>
<apply id="sodium_current_m_gate_m_infinity_calculation">
<eq/>
<ci> m_infinity </ci>
<apply>
<divide/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 42.1 </cn>
</apply>
</apply>
<cn cellml:units="millivolt"> 4.3 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply id="sodium_current_m_gate_tau_m_calculation">
<eq/>
<ci> tau_m </ci>
<apply>
<plus/>
<apply>
<divide/>
<cn cellml:units="millisecond"> 4.3 </cn>
<apply>
<plus/>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 47.0 </cn>
</apply>
<cn cellml:units="millivolt"> 11.0 </cn>
</apply>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless"> 2.0 </cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dimensionless"> -2.0 </cn>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 47.0 </cn>
</apply>
</apply>
<cn cellml:units="millivolt"> 11.0 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<cn cellml:units="millisecond"> 0.1 </cn>
</apply>
</apply>
</math>
</component>
<component name="sodium_current_h_gate">
<variable units="dimensionless" public_interface="out" name="h"/>
<variable units="dimensionless" name="h_infinity"/>
<variable units="millisecond" name="tau_h"/>
<variable units="millivolt" public_interface="in" name="V"/>
<variable units="millisecond" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="sodium_current_h_gate_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> h </ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<ci> h_infinity </ci>
<ci> h </ci>
</apply>
<ci> tau_h </ci>
</apply>
</apply>
<apply id="sodium_current_h_gate_infinity_calculation">
<eq/>
<ci> h_infinity </ci>
<apply>
<divide/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 68.2 </cn>
</apply>
<cn cellml:units="millivolt"> 10.8 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply id="tau_h_calculation">
<eq/>
<ci> tau_h </ci>
<apply>
<divide/>
<cn cellml:units="millisecond"> 150.0 </cn>
<apply>
<plus/>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 80.0 </cn>
</apply>
<cn cellml:units="millivolt"> 19.0 </cn>
</apply>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless"> 2.0 </cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dimensionless"> -2.0 </cn>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 80.0 </cn>
</apply>
</apply>
<cn cellml:units="millivolt"> 19.0 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
</rdf:value>
<!-- The creator of the comment. -->
<dc:creator rdf:parseType="Resource">
<vCard:FN>Catherine Lloyd</vCard:FN>
</dc:creator>
</cmeta:comment>
</rdf:Description>
</rdf:RDF>
<component name="sodium_current">
<variable units="picoA" public_interface="out" name="i_Na"/>
<variable units="nanoS" name="g_Na" initial_value="60.0"/>
<variable units="millivolt" name="V_Na" initial_value="60.0"/>
<variable units="dimensionless" name="O"/>
<variable units="millisecond" public_interface="in" name="time"/>
<variable units="millivolt" public_interface="in" name="V"/>
<variable units="millimolar" public_interface="in" name="A"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="i_Na_calculation">
<eq/>
<ci> i_Na </ci>
<apply>
<times/>
<ci> g_Na </ci>
<ci> O </ci>
<apply>
<minus/>
<ci> V </ci>
<ci> V_Na </ci>
</apply>
</apply>
</apply>
<apply id="O_calculation">
<eq/>
<ci> O </ci>
<apply>
<power/>
<ci> A </ci>
<cn cellml:units="dimensionless"> 3.0 </cn>
</apply>
</apply>
</math>
</component>
<component name="A">
<variable units="millimolar" public_interface="out" name="A"/>
<variable units="millimolar_per_ms" public_interface="in" name="delta_A_rxn_1"/>
<variable units="millimolar_per_ms" public_interface="in" name="delta_A_rxn_4"/>
<variable units="millisecond" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="A_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>A</ci>
</apply>
<apply>
<plus/>
<ci>delta_A_rxn_1</ci>
<ci>delta_A_rxn_4</ci>
</apply>
</apply>
</math>
</component>
<component name="inhibited_A">
<variable units="millimolar" public_interface="out" name="inhibited_A"/>
<variable units="millimolar_per_ms" public_interface="in" name="delta_inhibited_A_rxn_1"/>
<variable units="millimolar_per_ms" public_interface="in" name="delta_inhibited_A_rxn_2"/>
<variable units="millisecond" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="inhibited_A_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>inhibited_A</ci>
</apply>
<apply>
<plus/>
<ci>delta_inhibited_A_rxn_1</ci>
<ci>delta_inhibited_A_rxn_2</ci>
</apply>
</apply>
</math>
</component>
<component name="D">
<variable units="millimolar" public_interface="out" name="D"/>
<variable units="millimolar_per_ms" public_interface="in" name="delta_D_rxn_3"/>
<variable units="millimolar_per_ms" public_interface="in" name="delta_D_rxn_4"/>
<variable units="millisecond" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="D_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>D</ci>
</apply>
<apply>
<plus/>
<ci>delta_D_rxn_3</ci>
<ci>delta_D_rxn_4</ci>
</apply>
</apply>
</math>
</component>
<component name="inhibited_D">
<variable units="millimolar" public_interface="out" name="inhibited_D"/>
<variable units="millimolar_per_ms" public_interface="in" name="delta_inhibited_D_rxn_2"/>
<variable units="millimolar_per_ms" public_interface="in" name="delta_inhibited_D_rxn_3"/>
<variable units="millisecond" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="inhibited_D_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>inhibited_D</ci>
</apply>
<apply>
<plus/>
<ci>delta_inhibited_D_rxn_2</ci>
<ci>delta_inhibited_D_rxn_3</ci>
</apply>
</apply>
</math>
</component>
<component name="reaction1">
<variable units="millimolar" public_interface="in" name="A"/>
<variable units="millimolar" public_interface="in" name="inhibited_A"/>
<variable units="per_millisecond" public_interface="out" name="k1" initial_value="0.3"/>
<variable units="per_millisecond" public_interface="out" name="k1_" initial_value="0.03"/>
<variable units="millimolar_per_ms" public_interface="out" name="delta_A_rxn_1"/>
<variable units="millimolar_per_ms" public_interface="out" name="delta_inhibited_A_rxn_1"/>
<variable units="millimolar_per_ms" name="rate"/>
<reaction reversible="yes">
<variable_ref variable="A">
<role stoichiometry="1" direction="forward" delta_variable="delta_A_rxn_1" role="reactant"/>
</variable_ref>
<variable_ref variable="inhibited_A">
<role stoichiometry="1" direction="forward" delta_variable="delta_inhibited_A_rxn_1" role="product"/>
</variable_ref>
<variable_ref variable="rate">
<role role="rate">
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci> rate </ci>
<apply>
<plus/>
<apply>
<times/>
<ci>k1</ci>
<ci>A</ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci>k1_</ci>
<ci>inhibited_A</ci>
</apply>
</apply>
</apply>
</apply>
</math>
</role>
</variable_ref>
</reaction>
</component>
<component name="reaction2">
<variable units="millimolar" public_interface="in" name="inhibited_A"/>
<variable units="millimolar" public_interface="in" name="inhibited_D"/>
<variable units="millivolt" public_interface="in" name="V"/>
<variable units="per_millisecond" public_interface="in" name="k1"/>
<variable units="per_millisecond" public_interface="in" name="k1_"/>
<variable units="per_millisecond" public_interface="in" name="k3"/>
<variable units="per_millisecond" public_interface="in" name="k3_"/>
<variable units="millisecond" public_interface="out" name="alpha"/>
<variable units="millisecond" public_interface="out" name="beta"/>
<variable units="dimensionless" name="a"/>
<variable units="millimolar_per_ms" public_interface="out" name="delta_inhibited_A_rxn_2"/>
<variable units="millimolar_per_ms" public_interface="out" name="delta_inhibited_D_rxn_2"/>
<variable units="millimolar_per_ms" name="rate"/>
<reaction reversible="yes">
<variable_ref variable="inhibited_A">
<role stoichiometry="1" direction="forward" delta_variable="delta_inhibited_A_rxn_2" role="reactant"/>
</variable_ref>
<variable_ref variable="inhibited_D">
<role stoichiometry="1" direction="forward" delta_variable="delta_inhibited_D_rxn_2" role="product"/>
</variable_ref>
<variable_ref variable="rate">
<role role="rate">
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci> rate </ci>
<apply>
<plus/>
<apply>
<divide/>
<apply>
<times/>
<ci>beta</ci>
<ci>inhibited_A</ci>
</apply>
<ci>a</ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci>alpha</ci>
<ci>a</ci>
<ci>inhibited_D</ci>
</apply>
</apply>
</apply>
</apply>
</math>
</role>
</variable_ref>
</reaction>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="alpha_calculation">
<eq/>
<ci> alpha </ci>
<apply>
<divide/>
<cn cellml:units="millisecond"> 10.0 </cn>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 6.0 </cn>
</apply>
</apply>
<cn cellml:units="millivolt"> 10.0 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply id="beta_calculation">
<eq/>
<ci> beta </ci>
<apply>
<divide/>
<cn cellml:units="millisecond"> 10.0 </cn>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 54.4 </cn>
</apply>
<cn cellml:units="millivolt"> 4.6 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply id="a_calculation">
<eq/>
<ci> a </ci>
<apply>
<power/>
<apply>
<divide/>
<apply>
<times/>
<ci> k1 </ci>
<ci> k3_ </ci>
</apply>
<apply>
<times/>
<ci> k1_ </ci>
<ci> k3 </ci>
</apply>
</apply>
<cn cellml:units="dimensionless"> 0.5 </cn>
</apply>
</apply>
</math>
</component>
<component name="reaction3">
<variable units="millimolar" public_interface="in" name="D"/>
<variable units="millimolar" public_interface="in" name="inhibited_D"/>
<variable units="per_millisecond" public_interface="out" name="k3" initial_value="0.001"/>
<variable units="per_millisecond" public_interface="out" name="k3_" initial_value="0.01"/>
<variable units="millimolar_per_ms" public_interface="out" name="delta_D_rxn_3"/>
<variable units="millimolar_per_ms" public_interface="out" name="delta_inhibited_D_rxn_3"/>
<variable units="millimolar_per_ms" name="rate"/>
<reaction reversible="yes">
<variable_ref variable="D">
<role stoichiometry="1" direction="forward" delta_variable="delta_D_rxn_3" role="reactant"/>
</variable_ref>
<variable_ref variable="inhibited_D">
<role stoichiometry="1" direction="forward" delta_variable="delta_inhibited_D_rxn_3" role="product"/>
</variable_ref>
<variable_ref variable="rate">
<role role="rate">
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci> rate </ci>
<apply>
<plus/>
<apply>
<times/>
<ci>k3</ci>
<ci>D</ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci>k3_</ci>
<ci>inhibited_D</ci>
</apply>
</apply>
</apply>
</apply>
</math>
</role>
</variable_ref>
</reaction>
</component>
<component name="reaction4">
<variable units="millimolar" public_interface="in" name="A"/>
<variable units="millimolar" public_interface="in" name="D"/>
<variable units="millisecond" public_interface="in" name="alpha"/>
<variable units="millisecond" public_interface="in" name="beta"/>
<variable units="millimolar_per_ms" public_interface="out" name="delta_A_rxn_4"/>
<variable units="millimolar_per_ms" public_interface="out" name="delta_D_rxn_4"/>
<variable units="millimolar_per_ms" name="rate"/>
<reaction reversible="yes">
<variable_ref variable="A">
<role stoichiometry="1" direction="forward" delta_variable="delta_A_rxn_4" role="product"/>
</variable_ref>
<variable_ref variable="D">
<role stoichiometry="1" direction="forward" delta_variable="delta_D_rxn_4" role="reactant"/>
</variable_ref>
<variable_ref variable="rate">
<role role="rate">
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci> rate </ci>
<apply>
<plus/>
<apply>
<times/>
<ci>alpha</ci>
<ci>D</ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci>beta</ci>
<ci>A</ci>
</apply>
</apply>
</apply>
</apply>
</math>
</role>
</variable_ref>
</reaction>
</component>
<component name="L_type_calcium_current">
<variable units="picoA" public_interface="out" name="i_Ca_L"/>
<variable units="millivolt" public_interface="out" name="V_Ca" initial_value="100.0"/>
<variable units="nanoS" name="g_Ca_L" initial_value="1.3"/>
<variable units="millisecond" public_interface="in" private_interface="out" name="time"/>
<variable units="millivolt" public_interface="in" private_interface="out" name="V"/>
<variable units="dimensionless" private_interface="in" name="m"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="i_Ca_L_calculation">
<eq/>
<ci> i_Ca_L </ci>
<apply>
<times/>
<ci> g_Ca_L </ci>
<apply>
<power/>
<ci> m </ci>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
<apply>
<minus/>
<ci> V </ci>
<ci> V_Ca </ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="L_type_calcium_current_m_gate">
<variable units="dimensionless" public_interface="out" name="m"/>
<variable units="dimensionless" name="m_infinity"/>
<variable units="millisecond" name="tau_m"/>
<variable units="millivolt" name="Vh" initial_value="40.0"/>
<variable units="millivolt" public_interface="in" name="V"/>
<variable units="millisecond" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="L_type_calcium_current_m_gate_m_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> m </ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<ci> m_infinity </ci>
<ci> m </ci>
</apply>
<ci> tau_m </ci>
</apply>
</apply>
<apply id="L_type_calcium_current_m_gate_m_infinity_calculation">
<eq/>
<ci> m_infinity </ci>
<apply>
<divide/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<minus/>
<ci> V </ci>
<ci> Vh </ci>
</apply>
</apply>
<cn cellml:units="millivolt"> 12.0 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply id="L_type_calcium_current_m_gate_tau_m_calculation">
<eq/>
<ci> tau_m </ci>
<apply>
<divide/>
<cn cellml:units="millisecond"> 5.0 </cn>
<apply>
<plus/>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 15.0 </cn>
</apply>
<cn cellml:units="millivolt"> 25.0 </cn>
</apply>
</apply>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 15.0 </cn>
</apply>
</apply>
<cn cellml:units="millivolt"> 25.0 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="T_type_calcium_current">
<variable units="picoA" public_interface="out" name="i_Ca_T"/>
<variable units="nanoS" name="g_Ca_T" initial_value="0.94"/>
<variable units="millisecond" public_interface="in" private_interface="out" name="time"/>
<variable units="millivolt" public_interface="in" private_interface="out" name="V"/>
<variable units="millivolt" public_interface="in" name="V_Ca"/>
<variable units="dimensionless" private_interface="in" name="m"/>
<variable units="dimensionless" private_interface="in" name="h"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="i_Ca_T_calculation">
<eq/>
<ci> i_Ca_T </ci>
<apply>
<times/>
<ci> g_Ca_T </ci>
<apply>
<power/>
<ci> m </ci>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
<ci> h </ci>
<apply>
<minus/>
<ci> V </ci>
<ci> V_Ca </ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="T_type_calcium_current_m_gate">
<variable units="dimensionless" public_interface="out" name="m"/>
<variable units="dimensionless" name="m_infinity"/>
<variable units="millisecond" name="tau_m"/>
<variable units="millivolt" public_interface="in" name="V"/>
<variable units="millisecond" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="T_type_calcium_current_m_gate_m_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> m </ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<ci> m_infinity </ci>
<ci> m </ci>
</apply>
<ci> tau_m </ci>
</apply>
</apply>
<apply id="T_type_calcium_current_m_gate_m_infinity_calculation">
<eq/>
<ci> m_infinity </ci>
<apply>
<divide/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<minus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 56.1 </cn>
</apply>
</apply>
<cn cellml:units="millivolt"> 10.0 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply id="T_type_calcium_current_m_gate_tau_m_calculation">
<eq/>
<ci> tau_m </ci>
<apply>
<plus/>
<apply>
<divide/>
<cn cellml:units="millisecond"> 7.0 </cn>
<apply>
<plus/>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 50.0 </cn>
</apply>
<cn cellml:units="millivolt"> 9.0 </cn>
</apply>
</apply>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 50.0 </cn>
</apply>
</apply>
<cn cellml:units="millivolt"> 9.0 </cn>
</apply>
</apply>
</apply>
</apply>
<cn cellml:units="millisecond"> 0.8 </cn>
</apply>
</apply>
</math>
</component>
<component name="T_type_calcium_current_h_gate">
<variable units="dimensionless" public_interface="out" name="h"/>
<variable units="dimensionless" name="h_infinity"/>
<variable units="millisecond" name="tau_h" initial_value="22.0"/>
<variable units="millivolt" public_interface="in" name="V"/>
<variable units="millisecond" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="T_type_calcium_current_h_gate_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> h </ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<ci> h_infinity </ci>
<ci> h </ci>
</apply>
<ci> tau_h </ci>
</apply>
</apply>
<apply id="T_type_calcium_current_h_gate_infinity_calculation">
<eq/>
<ci> h_infinity </ci>
<apply>
<divide/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 86.4 </cn>
</apply>
<cn cellml:units="millivolt"> 4.7 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="delayed_rectifier_K_channel_current">
<variable units="picoA" public_interface="out" name="i_K_dr"/>
<variable units="millivolt" public_interface="out" name="V_K" initial_value="-80.0"/>
<variable units="nanoS" name="g_K_dr" initial_value="20.0"/>
<variable units="second" public_interface="in" private_interface="out" name="time"/>
<variable units="millivolt" public_interface="in" private_interface="out" name="V"/>
<variable units="dimensionless" private_interface="in" name="n"/>
<variable units="dimensionless" private_interface="in" name="h"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="i_K_dr_calculation">
<eq/>
<ci> i_K_dr </ci>
<apply>
<times/>
<ci> g_K_dr </ci>
<apply>
<power/>
<ci> n </ci>
<cn cellml:units="dimensionless"> 4.0 </cn>
</apply>
<ci> h </ci>
<apply>
<minus/>
<ci> V </ci>
<ci> V_K </ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="delayed_rectifier_K_channel_current_n_gate">
<variable units="dimensionless" public_interface="out" name="n"/>
<variable units="dimensionless" name="n_infinity"/>
<variable units="millisecond" name="tau_n"/>
<variable units="millivolt" public_interface="in" name="V"/>
<variable units="millisecond" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="delayed_rectifier_K_channel_current_n_gate_n_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> n </ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<ci> n_infinity </ci>
<ci> n </ci>
</apply>
<ci> tau_n </ci>
</apply>
</apply>
<apply id="delayed_rectifier_K_channel_current_n_gate_n_infinity_calculation">
<eq/>
<ci> n_infinity </ci>
<apply>
<divide/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 25.0 </cn>
</apply>
</apply>
<cn cellml:units="millivolt"> 15.0 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply id="delayed_rectifier_K_channel_current_n_gate_tau_n_calculation">
<eq/>
<ci> tau_n </ci>
<apply>
<plus/>
<apply>
<divide/>
<cn cellml:units="millisecond"> 15.0 </cn>
<apply>
<plus/>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 30.0 </cn>
</apply>
<cn cellml:units="millivolt"> 15.0 </cn>
</apply>
</apply>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 30.0 </cn>
</apply>
</apply>
<cn cellml:units="millivolt"> 15.0 </cn>
</apply>
</apply>
</apply>
</apply>
<cn cellml:units="millisecond"> 1.0 </cn>
</apply>
</apply>
</math>
</component>
<component name="delayed_rectifier_K_channel_current_h_gate">
<variable units="dimensionless" public_interface="out" name="h"/>
<variable units="dimensionless" name="h_infinity"/>
<variable units="millisecond" name="tau_h" initial_value="1000.0"/>
<variable units="millivolt" public_interface="in" name="V"/>
<variable units="millisecond" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="delayed_rectifier_K_channel_current_h_gate_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> h </ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<ci> h_infinity </ci>
<ci> h </ci>
</apply>
<ci> tau_h </ci>
</apply>
</apply>
<apply id="delayed_rectifier_K_channel_current_h_gate_infinity_calculation">
<eq/>
<ci> h_infinity </ci>
<apply>
<plus/>
<apply>
<divide/>
<cn cellml:units="dimensionless"> 0.7 </cn>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 35.0 </cn>
</apply>
</apply>
<cn cellml:units="millivolt"> 10.0 </cn>
</apply>
</apply>
</apply>
</apply>
<cn cellml:units="dimensionless"> 0.3 </cn>
</apply>
</apply>
</math>
</component>
<component name="M_like_K_current">
<variable units="picoA" public_interface="out" name="i_M"/>
<variable units="nanoS" name="g_M" initial_value="4.0"/>
<variable units="millisecond" public_interface="in" private_interface="out" name="time"/>
<variable units="millivolt" public_interface="in" private_interface="out" name="V"/>
<variable units="millivolt" public_interface="in" name="V_K"/>
<variable units="dimensionless" private_interface="in" name="n"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="i_M_calculation">
<eq/>
<ci> i_M </ci>
<apply>
<times/>
<ci> g_M </ci>
<ci> n </ci>
<apply>
<minus/>
<ci> V </ci>
<ci> V_K </ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="M_like_K_current_n_gate">
<variable units="dimensionless" public_interface="out" name="n"/>
<variable units="dimensionless" name="n_infinity"/>
<variable units="millisecond" name="tau_n"/>
<variable units="millivolt" public_interface="in" name="V"/>
<variable units="millisecond" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="M_like_K_current_n_gate_n_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> n </ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<ci> n_infinity </ci>
<ci> n </ci>
</apply>
<ci> tau_n </ci>
</apply>
</apply>
<apply id="M_like_K_current_n_gate_n_infinity_calculation">
<eq/>
<ci> n_infinity </ci>
<apply>
<divide/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 37.0 </cn>
</apply>
</apply>
<cn cellml:units="millivolt"> 4.0 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply id="M_like_K_current_n_gate_tau_n_calculation">
<eq/>
<ci> tau_n </ci>
<apply>
<divide/>
<cn cellml:units="millisecond"> 80.0 </cn>
<apply>
<plus/>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 30.0 </cn>
</apply>
<cn cellml:units="millivolt"> 15.0 </cn>
</apply>
</apply>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 30.0 </cn>
</apply>
</apply>
<cn cellml:units="millivolt"> 15.0 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="inward_rectifier_K_current">
<variable units="picoA" public_interface="out" name="i_ir"/>
<variable units="nanoS" name="g_ir" initial_value="1.71"/>
<variable units="millisecond" public_interface="in" private_interface="out" name="time"/>
<variable units="millivolt" public_interface="in" private_interface="out" name="V"/>
<variable units="millivolt" public_interface="in" name="V_K"/>
<variable units="dimensionless" private_interface="in" name="n_infinity"/>
<math xmlns="http://www.w3.org/1998/irath/irathirL">
<apply id="i_ir_calculation">
<eq/>
<ci> i_ir </ci>
<apply>
<times/>
<ci> g_ir </ci>
<ci> n_infinity </ci>
<apply>
<minus/>
<ci> V </ci>
<ci> V_K </ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="inward_rectifier_K_current_n_gate">
<variable units="dimensionless" public_interface="out" name="n_infinity"/>
<variable units="millivolt" public_interface="in" name="V"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="inward_rectifier_K_current_n_gate_n_infinity_calculation">
<eq/>
<ci> n_infinity </ci>
<apply>
<plus/>
<apply>
<times/>
<cn cellml:units="dimensionless"> 0.8 </cn>
<apply>
<divide/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<ci> V </ci>
<cn cellml:units="millivolt"> 80.0 </cn>
</apply>
<cn cellml:units="millivolt"> 12.0 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<cn cellml:units="dimensionless"> 0.2 </cn>
</apply>
</apply>
</math>
</component>
<component name="inward_leak_current">
<variable units="picoA" public_interface="out" name="i_d"/>
<variable units="nanoS" name="g_d" initial_value="0.044"/>
<variable units="millisecond" public_interface="in" name="time"/>
<variable units="millivolt" public_interface="in" name="V"/>
<variable units="millivolt" public_interface="in" name="V_Ca"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="i_d_calculation">
<eq/>
<ci> i_d </ci>
<apply>
<times/>
<ci> g_d </ci>
<apply>
<minus/>
<ci> V </ci>
<ci> V_Ca </ci>
</apply>
</apply>
</apply>
</math>
</component>
<group>
<relationship_ref relationship="containment"/>
<component_ref component="membrane">
<component_ref component="sodium_current"/>
<component_ref component="L_type_calcium_current">
<component_ref component="L_type_calcium_current_m_gate"/>
</component_ref>
<component_ref component="T_type_calcium_current">
<component_ref component="T_type_calcium_current_m_gate"/>
<component_ref component="T_type_calcium_current_h_gate"/>
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<component_ref component="delayed_rectifier_K_channel_current">
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<rdf:type rdf:resource="http://www.cellml.org/bqs/1.0#Person"/>
<vCard:N rdf:resource="rdf:#663e6803-4a84-4450-b085-c284d019d158"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#58709ae9-167b-4a8f-be27-a213691b51f8">
<dcterms:W3CDTF>2002-07-19</dcterms:W3CDTF>
</rdf:Description>
<rdf:Description rdf:about="rdf:#37157642-9ea6-4178-8fd6-69312c54d0d8">
<vCard:N rdf:resource="rdf:#0876e16f-0dee-46c9-b639-ccc4dfc21d89"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#5c58826d-d388-4580-b385-f6310ee41e55">
<vCard:Given>Andrew</vCard:Given>
<vCard:Family>LeBeau</vCard:Family>
<vCard:Other>P</vCard:Other>
</rdf:Description>
</rdf:RDF>
</model>
